Printers are useful for producing printed images of a wide range of types. Printers print on receivers (or “imaging substrates”), such as pieces or sheets of paper or other planar media, glass, fabric, metal, or other objects. Printers typically operate using subtractive color: a substantially reflective receiver is overcoated image-wise with cyan (C), magenta (M), yellow (Y), black (K), and other colorants. Various schemes can be used to process images to be printed. Printers can operate by inkjet, electrophotography, and other processes.
In the electrophotographic (EP) process, an electrostatic latent image is formed on a photoreceptor by uniformly charging the photoreceptor and then discharging selected areas of the uniform charge to yield an electrostatic charge pattern corresponding to the desired image (a “latent image”). After the latent image is formed, charged toner particles are brought into the vicinity of the photoreceptor and are attracted to the latent image to develop the latent image into a visible image. Note that the visible image may not be visible to the naked eye depending on the composition of the toner particles (e.g., clear toner).
After the latent image is developed into a visible image on the photoreceptor, a suitable receiver is brought into juxtaposition with the visible image. A suitable electric field is applied to transfer the toner particles of the visible image to the receiver to form the desired print image on the receiver. The receiver is then removed from its operative association with the photoreceptor and subjected to heat or pressure to permanently fix (“fuse”) the print image to the receiver. Plural print images, e.g., of separations of different colors, are overlaid on one receiver before fusing to form a multi-color print image on the receiver.
Printers typically transport the receiver past an imaging element (e.g., the photoreceptor) to form the print image. The direction of travel of the receiver is referred to as the slow-scan, process, or in-track direction. This is typically the vertical (Y) direction of a portrait-oriented receiver. The direction perpendicular to the slow-scan direction is referred to as the fast-scan, cross-process, or cross-track direction, and is typically the horizontal (X) direction of a portrait-oriented receiver. “Scan” does not imply that any components are moving or scanning across the receiver; the terminology is conventional in the art.
Various components used in printing processes, such as belts and drums, can have mechanical or electrical characteristics that result in periodic objectionable non-uniformities in print images, such as streaks (extending in-track), bands (extending cross-track) and irregular two dimensional patterns. For example, drums can experience run out: they can be elliptical rather than circular in cross-section, or can be mounted slightly off-center, so that the radius of the drum at a particular angle with the horizontal varies over time. Likewise, they may have irregular deformities to their shape or surface characteristics. Belts can have thicknesses that vary across their widths (cross-track) or along their lengths (in-track). Damped springs for mounting components can experience periodic vibrations, causing the spacing between the mounted components to change over time. These variations can be periodic in nature, that is, each variation cycles through various magnitudes repeatedly in sequence, at a characteristic and generally fixed frequency. The variations can also be non-periodic. For example, two cooperating drums with periodic non-uniformities at frequencies whose ratio is irrational will produce a non-periodic nonuniformity between them.
Various schemes have been proposed for correcting image artifacts in prints, including those resulting from these mechanical or electrical variations.
U.S. Pat. No. 7,058,325 to Hamby et al. deposits a test patch, measures its density, and corrects using a feedback or feedforward control routine. U.S. Pat. No. 5,546,165 to Rushing et al. scans a document to be reproduced, and the resulting reproduction, and adjusts for calibration errors in the processing of the image of the document. U.S. Pat. No. 6,885,833 to Stelter et al. detects variations and periodicities of densities in a print. U.S. Pat. No. 7,755,799 to Paul et al. also measures test patches, and uses a defect once-around signal to synchronize the measurements to the rotation of the drum. The once-around signal is derived from an optical sensor monitoring the drum's position. Paul describes that the phase of a periodic banding defect (an artifact extending cross-track) is difficult to measure because, unlike frequency, it varies from page to page. U.S. Pat. No. 7,382,507 to Wu analyzes test patterns to generate image quality defect records and stores the records in a database for later analysis.
However, often times the non-uniformities are somewhat irregular rather than a smooth sinusoidal function. This is especially evident when considering two dimensional non-uniformities in dimensional or surface properties. For these cases, a map of one period of rotation of the rotating member can best represent the variation. This can be either a look up table or by applying functions that estimate variation in one or both directions.